RAID 1 = mirroring. Data is copied across both drives. This is at the lower end of what could be called "backup". if a disk fails, take the failed disk out, put another of the same type in and rebuild the mirror. If the NAS itself fails, take the disks out and put them in another NAS. Bear in mind that ALL data is copied, including viruses and malware. However in a proper off-site backup, all data including viruses (like the ones that trigger on certain dates) are also backed up and taken off site. IIRC, failure of the NAS and one of the disks (power surge maybe) still not the end as , as long as one of the disks is still usable you can still replace the NAS and faulty drive and rebuild the mirror. No sure about taking the disk about and putting it in a caddy though as I've never had reason to try. Remember also that you get half the storage you pay for.
RAID5 is a bit more interesting. this stripes the data across drives with extra parity data written so that any drive can be lost but the system can still run. You need a minimum of 3 disks and the storage you will actually get is n-1 disks (eg 3 *1TB disks gives you 2TB storage). data striping also means less spin time, so performance is faster and, there being less wear due to less physical movement, disks are less likely to fail. NAS boxes tend to be a bit more expensive as there's more bays. Typically more than 2 bays is at least 4, which means you may have access to..
..all RAID levels support +1 (although your chosen NAS box might not). This means that the system can support a hot spare, a disk configured, powered down but ready for action. A disk fails, the hot spare powers up and builds itself as a copy of the failed disk. Technically, this works while the system is live, but performance degrades so much that, IME, the host system is unusable till the rebuild is complee and taking it off-line is usually a better bet.
IOt does mean though that your system can support 2 failed disks and continue to run (RAID 5 will run with 1 failed drive, the hot spare kicks in and you can still have another failure). Again though, this means you're paying for storage you may never use.
Also RAID1+1 may need manual intervention to rebuild the mirror
RAID systems are far from flaky as a rule